Geodesic
Matsuki's Double Coset Decomposition via Gradient Maps
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 555-58.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let G be a real-reductive Lie group and let G1 and G2 be two subgroups given by involutions. We show how the technique of gradient maps can be used in order to obtain a new proof of Matsuki's parametrization of the closed double cosets G1 \ G / G2 by Cartan subsets. We also describe the elements sitting in non-closed double cosets.
Classification : 22E15, 22E46
Mots-clés : Reductive Lie group, involution, orbit structure, gradient map, slice theorem, symmetric Lie algebra 
@article{JLT_2008_18_3_JLT_2008_18_3_a4,
     author = {C. Miebach },
     title = {Matsuki's {Double} {Coset} {Decomposition} via {Gradient} {Maps}},
     journal = {Journal of Lie theory},
     pages = {555--58},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a4/}
}
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C. Miebach . Matsuki's Double Coset Decomposition via Gradient Maps. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 555-58. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a4/